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The effect of microscopic friction and size distributions on conditional probability distributions in soft particle packings

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Abstract

Employing two-dimensional molecular dynamics (MD) simulations of soft particles, we study their non-affine responses to quasi-static isotropic compression where the effects of microscopic friction between the particles in contact and particle size distributions are examined. To quantify complicated restructuring of force-chain networks under isotropic compression, we introduce the conditional probability distributions (CPDs) of particle overlaps such that a master equation for distribution of overlaps in the soft particle packings can be constructed. From our MD simulations, we observe that the CPDs are well described by q-Gaussian distributions, where we find that the correlation for the evolution of particle overlaps is suppressed by microscopic friction, while it significantly increases with the increase of poly-dispersity.

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Notes

  1. The number of particles and size ratios of poly-dispersed particles are resembling the recent experiments of wooden cylinders [8].

  2. We confirmed that static packings prepared with longer length scales, \(\lambda =10^3\bar{\sigma }\) and \(10^4\bar{\sigma }\), give the same results concerning their critical scaling near jamming [10], while we cannot obtain the same results with a shorter length scale, \(\lambda =10\bar{\sigma }\).

  3. Here, \(p/k_\mathrm {n}\) is dimensionless in two dimensions and the scaled distances for radial distribution functions, g(r), are defined as \(r\equiv d_{ij}/(R_i+R_j)\).

  4. Because every acceleration is lower than the threshold, the viscous forces are negligible, while they play an important role during the relaxation process.

  5. Such a discontinuity is specific to static packings, where a corresponding gap has been observed in a radial distribution function in a glass with zero-temperature [12].

  6. From the Chapman–Kolmogorov equation (9), \(P_{\phi +\delta \phi }(\xi ') = \int _{-\infty }^\infty \delta (\xi '-\xi ^\mathrm {affine})P_\phi (\xi )\mathrm{d}\xi = \int _{-\infty }^\infty \delta (\xi '-B_a\gamma -\xi )P_\phi (\xi )\mathrm{d}\xi = P_\phi (\xi '-B_a\gamma )\).

  7. B(x, y) is the beta function.

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Acknowledgments

We thank M. Tolomeo, V. Richefeu, G. Combe, and G. Viggiani for fruitful discussions. This work was financially supported by the NWO-STW VICI Grant 10828, the World Premier International Research Center Initiative (WPI), Ministry of Education, Culture, Sports, Science, and Technology, Japan (MEXT), and Kawai Foundation for Sound Technology & Music. This work was also supported by Grant-in-Aid for Scientific Research B (Grants Nos. 16H04025 and 26310205) and Grant-in-Aid for Research Activity Start-up (Grant No. 16H06628) from the Japan Society for the Promotion of Science (JSPS). A part of numerical computation has been carried out at the Yukawa Institute Computer Facility, Kyoto, Japan.

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Authors and Affiliations

  1. WPI Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

    Kuniyasu Saitoh

  2. Faculty of Engineering Technology, MESA+, University of Twente, Drienerlolaan 5, 7522 NB, Enschede, The Netherlands

    Vanessa Magnanimo & Stefan Luding

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  1. Kuniyasu Saitoh
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  2. Vanessa Magnanimo
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  3. Stefan Luding
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Correspondence to Kuniyasu Saitoh.

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Saitoh, K., Magnanimo, V. & Luding, S. The effect of microscopic friction and size distributions on conditional probability distributions in soft particle packings. Comp. Part. Mech. 4, 409–417 (2017). https://doi.org/10.1007/s40571-016-0138-z

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